The largest angle is opposite to the longest side.
∠ 3, ∠ 1, ∠ 2
Practice makes perfect
From the given diagram, we can copy the following triangle.
To order the angles of the triangle from largest to smallest, let's recall what Theorem 5.9 states.
If one side of a triangle
is greater than the other side,
then the angle opposite to the longer side
has a greater measure than the angle
opposite to the shorter side.
As we can see on the diagram, the longest side measures 0.5 mi and the angle opposite to it is ∠ 3. Hence, ∠ 3 is the largest angle. The second longest side has the measure of 0.45 mi. It is opposite to ∠ 1, so this angle comes second. Finally, side that measures 0.4 mi is the shortest, so angle ∠ 2 is opposite and is the smallest.
∠ 3> ∠ 1> ∠ 2
The order of the angles from the largest to the smallest is the following.
∠ 3, ∠ 1, ∠ 2
